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The Last-Mile Delivery Process with Trucks and Drones Under Uncertain Energy Consumption

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Abstract

We address the problem of delivering parcels in an urban area, within a given time horizon, by conventional vehicles, i.e., trucks, equipped with drones. Both the trucks and the drones perform deliveries, and the drones are carried by the trucks. We focus on the energy consumption of the drones that we assume to be influenced by atmospheric events. Specifically, we manage the delivery process in a such a way as to avoid energy disruption against adverse weather conditions. We address the problem under the field of robust optimization, thus preventing energy disruption in the worst case. We consider several polytopes to model the uncertain energy consumption, and we propose a decomposition approach based on Benders’ combinatorial cuts. A computational study is carried out on benchmark instances. The aim is to assess the quality of the computed solutions in terms of solution reliability, and to analyze the trade-off between the risk-adverseness of the decision maker and the transportation cost.

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Acknowledgements

The authors would like to thank the anonymous referees for their constructive comments and useful suggestions.

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Authors and Affiliations

  1. Istituto di Calcolo e Reti ad Alte Prestazioni, Consiglio Nazionale delle Ricerche, Rende, Italy

    Luigi Di Puglia Pugliese

  2. Department of Mechanical, Energy and Management Engineering, University of Calabria, Rende, Italy

    Francesca Guerriero

  3. Dipartimento di Informatica, University of Pisa, Pisa, Italy

    Maria Grazia Scutellá

Authors
  1. Luigi Di Puglia Pugliese
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  2. Francesca Guerriero
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  3. Maria Grazia Scutellá
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Correspondence to Luigi Di Puglia Pugliese.

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Communicated by Jörg Rambau.

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Di Puglia Pugliese, L., Guerriero, F. & Scutellá, M.G. The Last-Mile Delivery Process with Trucks and Drones Under Uncertain Energy Consumption. J Optim Theory Appl 191, 31–67 (2021). https://doi.org/10.1007/s10957-021-01918-8

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  • DOI: https://doi.org/10.1007/s10957-021-01918-8

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